Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T06:30:32.463Z Has data issue: false hasContentIssue false
  • English
  • Français

A Unified Creep-Cyclic Plasticity Theory of Endochronic Viscoplasticity with Applications in 304 Stainless Steel

Published online by Cambridge University Press:  05 May 2011

C. F. Lee ,
H. T. Shen  and
W. T. Peng
C. F. Lee*
Affiliation:
Department of Engineering Science, National Cheng Kung University, Tainai, Taiwan 70101, R.O.C.
H. T. Shen*
Affiliation:
Product R&D Center V, Wistron Corporation
W. T. Peng*
Affiliation:
Civil/Structure Section, Engineering Department, Kang-Chuan Engineering, Co., Ltd.
*
*Professor
**Associate Technical Director
**Civil/Structure Section Chief
Get access

Abstract

In this paper, a unified creep-cyclic plasticity theory of endochronic viscoplasticity is established, in which the computations in the cyclic stress-strain responses of fatigue loading and the creep strain responses of general thermal/creep loading histories are integrated.

Based on the relationship of convolutional integral between the relaxation modulus function ρ(Z) and the creep compliance function J(Z), and the given functional form of ρ(Z) obtained from the cyclic hysteresis loop; an explicit functional form of J(Z) can be generated numerically which covers creep response from the primary creep stage to the steady creep stage. As a consequence, the conventional cyclic stress-strain curve, the Bailey-Norton creep law and the power law of steady creep rate are interrelated.

Four experiments of 304 stainless steel at about 0.52 homologous temperature and under constant or variable amplitude loading histories are investigated. The success in the unified computational methodology is demonstrated by the well agreement between the computational results and the experimental data.

Keywords

Endochronic viscoplasticityCreepCyclic stress-strain curveBailey-Norton creep lawPower law of steady creep rate.
Type
Articles
Information
Journal of Mechanics , Volume 19 , Issue 4 , December 2003 , pp. 443 - 453
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Kraus, H., Creep Analysis, JohnWiley & Sons N.Y., USA (1980).Google Scholar
2.Lau, J. H., Wong, C. P., Prince, J. L., and Nakayama, W., Electronic Packaging: Design, Materials, Process, and Reliability, McGraw-Hill Comp. Inc., USA (1998).Google Scholar
3.Lau, J. H., and Pao, Y H.,Solder Joint Reliability of BGA, CSP Flip Chip, and Fine Pitch SMT Assemblies, Chap. 4, McGraw-Hill Comp. Inc., USA, pp. 125–132 (1997).Google Scholar
4.Frear, D. R., Jones, W.B., and Kinsman, K.R., Solder Mechanics: A State of the Art Assessment, TMS Pub. Co., USA (1991).Google Scholar
5.Valanis, K. C., “A Theory of Viscoplasticity without a Yield Surface, Part I, General Theory, II, Application to Mechanical Behavior of Metal,” Archives of Mechanics, pp.517–551 (1971).Google Scholar
6.Miller, A. K., The MATMOD Equations, in Unified Constitutive Equations for Creep and Plasticity, Chap. 3., ed., Miller, A. K., Elsevier Appliced Science N.Y, USA (1987).CrossRefGoogle Scholar
7.Chaboche, J. L., “Constitutive Equations for Cyclic Plasticity and Cyclic Viscoplasticity,” Int. J. Plasticity, 5(3), pp. 247–302 (1989).Google Scholar
8.Mc Dowell, D. L.Miller, M. P., and Brooks, D. C., “A Unified Creep-Plasticity Theory for Solder Alloys,” Fatigue of Electronic Materials, ASTM STP 1153, pp. 42–59(1994).CrossRefGoogle Scholar
9.Desai, C. S., Basaran, C, Dichengh, T., and Prince, J. L., “Thermomechanical Analysis in Electronic Packaging with Unified Constitutive Model for Materials and Interfaces,” IEEE Trans. Component Packaging and Manufacturing Technology, Part B, 21, pp. 87–97 (1998).CrossRefGoogle Scholar
10.Lee, C F., and Hsiao, L. T., “EndoFEM Crack Closure Analysis of AL2024-T3 CCT Specimen under All Tension Fatigue Loading,” The Chinese Journal of Mechanics, 16(4), pp. 349–361 (2000).Google Scholar
11.Lee, C F., “A Simple Endochronic Transient Creep Model of Metals with Application to Variable Temperature Creep,” Int. J. Plasticity, 14(2), pp. 239–253 (1996).Google Scholar
12.Valanis, K.C and Lee, C F., “Endochronic Theory of Cyclic Plasticity with Applications,” ASME J. Appl. Mechanics, 51, pp. 367–374, (1984).CrossRefGoogle Scholar
13.Hopkins, I. L., and Hamming, R. W., “On Creep and Relaxation,” J. Appl. Phys., 28, p. 906 (1957) and 29, p. 742 (1958).Google Scholar
14.Kraus, A. S. and Eyring, H., Deformation Kinetics, John Wiley &Sons N.Y. (1980).Google Scholar
15.Comm, J. M., “Appendix: Material Property Data for Elastic-Plastic-Creep Analysis of Benchmark Problems,” Pressure Vessels and Piping: Verification and Qualification of Inelastic Analysis Computer Programs, ed., Comm, J. M. and Wright, W. B., ASME, pp. 99–109 (1975).Google Scholar
16.Murakami, S., Olmo, N. and Tagami, H., “Experimental Evaluation of Creep Constitutive Equations for Type 304 Stainless Steel under Nonsteady Multiaxial States of Stress,” ASME J.Eng. Materials and Technology, 108, pp. 119–126(1986).CrossRefGoogle Scholar
17.Lee, C. F., “A Systematic Method of Determining Material Function in the Endochronic Plasticity,” J. of the Chinese Society of Mech. Eng., 8(6), pp. 419–430 (1987).Google Scholar
18.Lee, C F., “A Simple Endochronic Creep Modeling and Its Computational Implementation,” Chinese J. of Mechanics, 7(1), pp. 21–32 (1991).Google Scholar